Q: What is the differential form of following equation ie square of volume plus square of pressure plus cube of temperature?

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No. For a gas, temperature also comes into the equation.

its pressure between suction and discharge flow...

Yes.The amount of gas is determined by its pressure, volume, and temperature. The equation is:PV = nRTwhere:P = pressure, measured in pascals (the SI derived unit of pressure)V = volumen = amount of substance of gas (moles)R = universal gas constantT = temperature

I suppose you mean the formula for the variation in pressure. The simplest expression of this is, at a fixed temperature,and for a given mass of gas, pressure x volume = constant. This is known as Boyle's Law. If the temperature is changing, then we get two relations: 1. If the pressure is fixed, volume = constant x temperature (absolute) 2. If the volume is fixed, pressure = constant x temperature (absolute) These can be combined into the ideal gas equation Pressure x Volume = constant x Temperature (absolute), or PV = RT where R = the molar gas constant. (Absolute temperature means degrees kelvin, where zero is -273 celsius)

I guess you're talking about the PV=nRT equation; well the volume of a gas depends on the temperature so of course the temperature must be kept constant or your pressure will be affected. The moles of the gas will also affect the pressure. Usually this equation is used to calculate the number of moles it will take to occupy a certain volume or vice versa at standard temperature and pressure: 1 atm and 0 degrees Celcius.

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No. For a gas, temperature also comes into the equation.

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